Pith Number

pith:WDJF47EU

pith:2026:WDJF47EUHVB62TFAP7YZPX6PBR

not attested not anchored not stored refs pending

Tropical Fermat--Weber Problems over Non-Finite Data and their Inverse Formulations

John Sabol, Ruriko Yoshida

arxiv:2606.27503 v1 · 2026-06-25 · math.CO · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WDJF47EUHVB62TFAP7YZPX6PBR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-29T00:14:08.431499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0d25e7c943d43ed4ca07ff197dfcf0c528c997c2687e8de33f22eeaebea1d2a

Aliases

arxiv: 2606.27503 · arxiv_version: 2606.27503v1 · doi: 10.48550/arxiv.2606.27503 · pith_short_12: WDJF47EUHVB6 · pith_short_16: WDJF47EUHVB62TFA · pith_short_8: WDJF47EU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WDJF47EUHVB62TFAP7YZPX6PBR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b0d25e7c943d43ed4ca07ff197dfcf0c528c997c2687e8de33f22eeaebea1d2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2727e97492a07904ff175653c7b930fe8de94aa7e639f0b03f95c80c1cd506a2",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-25T19:37:48Z",
    "title_canon_sha256": "32a78feee61370db85573fce8958f312a03ac22c97a8a8a49af695b0f5ac0986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27503",
    "kind": "arxiv",
    "version": 1
  }
}